Question

Solve the following quadratic equations by factorization:x+3 / x+2=3x-7 / 2x-3

Answer 1

x = 5 or x = -1 if (x + 3)/(x + 2)  = (3x - 7/(2x - 3)

Step-by-step explanation:

(x + 3)/(x + 2)  = (3x - 7/(2x - 3)

=> (x + 3)(2x - 3) = (3x - 7)(x + 2)

=> 2x²  + 3x - 9 = 3x² - x - 14

=> x² - 4x - 5 = 0

=> x² +x - 5x - 5 = 0

=> x(x + 1) - 5(x + 1) = 0

=> (x - 5)(x + 1) = 0

=> x = 5 or x = -1

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Answer 2

$\large \bf \red{ Given \: equation : }\\ \large\boxed{ \bf \orange{\frac{x + 3}{ x+ 2} = \frac{3x - 7}{2x - 3}}} \\ \\ \bf By \: cross \: multipy \\ \\\bf (x + 3)(2x - 3) = (x + 2)(3x - 7) \\ \\\bf 2 {x}^{2} - 3x + 6x - 9 = 3 {x}^{2} - 7x + 6x - 14 \\ \\ \bf2 {x}^{2} + 3x - 9 = 3 {x}^{2} - x - 14 \\ \\ \bf{x}^{2} - 4x - 5 = 0$

By splitting middle term :

$\bf {x}^{2} - 5x +x - 5 = 0\\ \\\bf x(x - 5) 1( x- 5) = 0 \\ \\ \bf(x + 1)( x -5) = 0 \\ \\\large \boxed{\bf \blue{ x =- 1} }\\ \bf or \\ \large\boxed{ \bf \green{ x = 5}}$